z= ((3+4i)(12-5i))/(2+i) a. |z| ? b. Re (z) and Im (z)?

Expanding the numerator







 

        

In OPQ, o = 870 inches, P = 80 degrees, and Q = 9 degrees. Find the length of p to the nearest 10th of an inch.

We'll denote the measure of angle X as

In any triangle the sum of the angles is 180 degrees, so

so we know

Now using the Law of Sines we write:



which leads to

The function f(x)=2x/3x-5 is one-to-one. find its inverse and check your answer

To find the inverse we can solve for x to convert it to the dependent variable:










Once their roles have reversed, the resulting expression is the inverse:

To check we take the two appropriate inverses to see if they each recover the input (i.e. x).

Checking...

If $1000 is invested in an account paying 12% annually compounded continously, how long will it take to double the investment?

For continuous compounding we use:


so we can write:



taking the natural log of both sides leads to



so time is about 5.78 years

solve the equation ln(x)- ln (x-3) = ln(5)

combining logs...



raising e to both sides of the equation...

which leads to...




and so...

Write the expression in the form a + bi, where a and b are real numbers. sqrt(-1)/( sqrt(-81)sqrt(-36))

Solve: log(x+4) + log(x)=9

Combining into one log...




raise 10 to both sides of the equation...



After solving we note that only positive numbers are solutions (Why?)

Solve: 2sec²θ+5tanθ=3

find reference angle for 215 degrees

so our angle is in Quad III
and so

Simplify: (sin(f+g)+sin(f-g))/(cos(f+g)+cos(f-g))

After expanding all 4 expressions using sum/difference identities we get:





which simplifies to...


 

and then to...

How do i find the measure of each angle for tan B = 0.6000

use inverse tangent function:

 

Find the intercepts and asymptotes. (If an answer does not exist, enter DNE.) r(x)=27/(x-3)^2

x-intercepts: Zeros only occur in the numerator so DNE
y-intercepts:
27/(-3)=-9
(0, -3)

VA:
x-3=0
x=3

HA:
as |x| --> oo
r --> 0
y=0

Triangle ABC is inscribed in a circle. AB is 12, AC is 6 and BC is 6 square root 3. Find arc BC.

These measures tell us that the triangle is a 30-60-90 triangle with a hypotenuse opposite the side AB and since we can see that arc BC is the arc of least measure, it must be 60 degrees

the cost of a telephone call is 5 pesos for the first three minutes and an additional of 2 pesos for each additional minute or fractional part thereof. find the cost of all call lasting: a) .5 min, b) 3 minutes, and c) 5 minutes

c(t)=5+2(t-3), t>3 

a) c(0.5)=5
b) c(3)=5
c) c(5)=5+2(5-3)=5+2(2)=9

How do you use the intermediate value theorem to show the polynomial function that has a zero in the given. [1.3, 1.9], f(x)= x^5-x^4+3x^3-4x^2-16x +15

f(1.3)=-5.112 (approx.)
f(1.9)=2.465 (approx.)
the theorem tells us that since there is a sign change for f on the interval there must be a zero on the interval

if 1/2 of an integer is added to 1/4 to the next consecutive integer the sum is 22.find the integer.

multiplying by 4...

√84 divided by 2√3